Chapter Regression-Based Models for Developing Commercial Demand Characteristics Investigation. Introduction Commercial area is another important area in terms of consume high electric energy in Japan. Therefore, as residential area, knowing demand characteristics of this area is valuable for utilities. In this regards, it is reported in some references [,] that commercial area can be correlated by meteorological parameters. However, determining such as what meteorological variables have contribution on commercial demand, how far the variables influence the demand, and etcetera is not an easy task, because it needs specific investigation through developing suitable analysis tool as an electricity demand may unique in one place. In this chapter, regression-based models are proposed to analyze specifically electricity demand characteristics particularly for Japanese commercial area. Beside different demand area, some extend from models in the Chapter are presented in this study for developing characteristics investigation. Here, demand regression models for two period levels based on different time length, namely half-year (two different models) and seasonal models (four different models) are composed for the task. They are developed from an initial model which is derived from all data or whole demand period with same explanation variables and process of validation. From models, the different commercial demand characteristics under certain periods are investigated. Typical characteristics of demand under two different conditions of temperature and humidity are derived through half-year models and analyzed. Next, by composing seasonal models, we continue to analyze characteristics of demand
more detail for each season. As CDD and HDD functions are implemented, several reference values of temperature T ref are tested and assessed in the models. The studied area is commercial demand in one city in Japan which is correlated by temperature and relative humidity as primary variables. Presented results can provide more insight about characteristics of demand particularly in seasonal levels. It is valuable in quantifying effect of driver variables to demand in certain periods, and in understanding situation of commercial demand more detail.. Data and Initial Demand Model.. Data As concerning data for models, in this study a demand for commercial area (Com. T), meteorological parameters, and holidays data are used. The analyzed demand is a total for two commercial demand places in one typical city in Japan. It is normalized hourly data from June 7 to November 9 which is offered by a utility. For meteorological parameters, we use temperature and relative humidity data for a representative city in Japan which is same area where the commercial demand data are collected. They are taken from Japan Meteorological Agency (JMA) open website []... Commercial Initial Demand Model As preliminary characteristics exploration, some figures involved demand and used variables are shown in relation to construct model. From histogram and scattered diagram in Fig.., it is seen that relationship between commercial demand Com. T and temperature T ( C) is not linear. Based on this fact, heating degree days HDD (HDD = max(t ref T, )) and cooling degree days CDD (CDD = max(t T ref )) variables are used in the composed model as in the previous chapter. For reference value of temperature (T ref ) for HDD and CDD, it is around 8 C []. However, as factors affect electricity demand characteristics in one place maybe unique, the using of suitable T ref in models may lead to optimum results. Therefore, four different T ref = T ref = T ref values (6 C, 7 C, 8 C, and 9 C) for composed models are calculated and then assessed by statistical tests. The tested range of T ref is shown by dotted lines on double 6
Chapter. Regression-Based Models for Developing Commercial Demand Characteristics Investigation arrow in Fig... Right side of the Tref shows commercial demand variation within hot temperature, and another side within cold temperature. To investigate effect of temperature to the commercial demand further, one hour previous temperature values (CDD(-) and HDD(-)) are also considered in each model as in [,]. Normalized hourly demand (commercial) T max = 6.7 C; T min = -.9 C; T mean = 8. C Tref tested - Temperature ( C) Fig.. Scattered diagram between commercial demand and temperature. Fig.. shows samples values of relative humidity RHD (%), and the demand in one week from (Friday) to 7 (Thursday) August 8. From the figure, both demand and Com. T RHD (%) 8 7 6 Holidays (- Aug 8)... Relative humidity (%) Normalized hourly demand (commercial) 9... 9 7 99 9 Hour ( Aug 8-7 Aug 8) Fig.. Samples of commercial demand variation and humidity for one week in August 8, and holidays between the period. 7
humidity values appear fluctuated. However, only electricity demand which has almost similar daily fluctuation. Fluctuation of the demand reaches maximum values around midday and evening. Besides, demand during holidays is lower than non-holidays. Normally, the nature of consumer and installed electric equipments are factors influence demand characteristics in one area such as commercial [6]. As an initial demand model, regression equation for all demand period is given in Eq. (.). It expresses normalized hourly demand for all data. CTEC CDD CDD ( ) HDD HDD( ) RHD.(.) 6 DH u t where CTEC is a commercial demand. α is intercept, and other α are regression coefficients. CDD(-) and HDD(-) are one hour previous data for CDD and HDD, respectively. A dummy variable for holidays (DH) is added in the model. DH value equals (one) expresses holidays, meanwhile the value (zero) is used for non-holidays (other days). Holidays includes not only weekends and national holidays, but also two nonnational holidays namely New Year event ( and January) and Obon Festival ( to 6 August). Though the latter two are not formal holidays in Japan, but working activity in that time is relatively small. To handle serial correlation, an autoregressive component in error term is employed in the models as in the Chapter. For simplicity of models, second order autoregressive error term is applied in this study. Models without autoregressive, and with first order autoregressive are also calculated as options for models.. Seasonal Demand Models for Characteristics Analysis To analyze Japanese commercial demand characteristics, regression based demand models for two period levels are composed which is developed from the initial model. Next, different demand characteristics for certain periods are investigated. We focus on exploring demand characteristics under two different conditions of temperature and humidity through half-year models. Then, by composing seasonal models, more specific characteristics analysis for each season is done. The same explanation variables with initial model are applied for models in both levels. Models are tested by Akaike Information Criterion and 8
Chapter. Regression-Based Models for Developing Commercial Demand Characteristics Investigation Schwarz Criterion (AIC and SC tests) to determine the best model in each level as in [,]. The adjusted coefficient of determination R of models is also assessed. Details about the procedure of developing models are explained in the following subsections... Proposed models for half-year period Seasonal periods are relatively varied for each place in the world. Particularly in Japan, climate condition in each place is quite different. However in one year, summer, autumn, winter, and spring are seasons occurred in Japan. Summer period is from June to August, and autumn is from September to November. Meanwhile winter period is from December to February, and spring is from March to May. Based on these seasons, initial model is developed into two types of half-year demand models, namely CTEChy and CTEChy. CTEChy model expresses commercial demand between June and November (summer and autumn), meanwhile CTEChy expresses demand between December and May (winter and spring). The similar condition of summer and autumn in terms of hot weather is the basis of categorization and on the contrary for winter and spring. The basic characteristics investigated through scattered diagram between demand and temperature for each half-year period is shown in Fig... In the figure, cold temperature in CTEChy appears mainly in November, meanwhile for hot temperature in CTEChy appears in May. T max = 6.7 C; T min =. C; T mean =. C T max = 9.9 C; T min = -.9 C; T mean =.7 C. Winter and Spring season, 8 6 Largely in November (a) Series: TEMPERATURE C Sample 77 Observations 76, Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis.78. 6.7..879 -.6698.9 Jarque-Bera Probability 88.9. 8 6.... 7. Series: TEMPERATURE C Sample 876 Observations 876 6. Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis.79. 9.9 -.9.9787.8797.667 Jarque-Bera Probability 9.886. Largely in May 6 8 6 8 6 8 6 Normalized hourly demand (commercial) Normalized hourly demand (commercial) Summer and Autumn season 8 Temperature ( C) 6 (b). - Temperature ( C) Fig.. Scattered diagram between commercial demand and temperature: (a) half-year, (b) half-year. 9
Temperature ( C) Chapter. Regression-Based Models for Developing Commercial Demand Characteristics Investigation Histograms of each linked temperature are shown in sub figures in the Fig... In November, mean temperature T mean (. C) is lower than minimum T ref, meanwhile in May, T mean (9.8 C) is obtained higher than maximum T ref. This condition underlies to use CDD and HDD as explanation variables in the half-year models to explore demand characteristics completely. For other variables (humidity and holidays) and validation processes of models, they are similar to the previous one. The electricity demand models for CTEChy and CTEChy are given as in Eqs. (.) and (.). CTEChy ˆ ˆ CDD ˆ CDD ˆ HDD ˆ ( ) HDD( ) ˆ RHD ˆ.. (.) 6 DH u t CTEChy ˆ ˆ CDD ˆ CDD ˆ HDD ˆ ( ) HDD( ) ˆ RHD ˆ.. (.) 6 DH u t where CTEChy and CTEChy are commercial demand for half-year and periods, respectively. ˆ is intercept, and other ˆ values are regression coefficients. Remaining variables are the same as in the initial model, Eq. (.). Considered the natural variation of temperature T, other two different half-year models (Category-) are also calculated. They express commercial demand between May and October, and between November and April. Under this category, all T mean for each month Half-year (Nov Apr) Half-year (May Oct) T min T mean T max - May Jun Jul Aug Sep Oct 6 Nov 7 Dec 8 Jan 9 Feb Mar Apr Month Fig.. Variation temperature values for each month from June to May 7.
within CTEChy a and CTEChy a periods become above and below T ref, respectively as shown in Fig... Because only a small part of the temperature values remained below or above T ref in the related periods, then it is proper to implement only CDD in CTEChy a, or HDD in CTEChy a model. Next, obtained output are compared each other to find optimum results... Proposed models for seasonal demand To reveal more demand characteristics, the preceding model is developed according to the seasons. Four different electricity demand models, that is summer (CTECSM), autumn (CTECA), winter (CTECW), and spring model (CTECS) are composed for exploring characteristics. Based on the season periods, November and May are months in autumn and in spring, respectively. Thus, two temperature variables (CDD and HDD) are used to compose autumn and spring models (CTECA and CTECS). For other models (CTECSM and CTECW), both in their periods have a few temperature values below (T min =. C) or above (T max =.8 C) of T ref range. However, for simplification, we consider only dominant temperature to compose CTECSM and CTECW models. The temperature range for each season is given in Fig... Regression equations for each commercial seasonal model are given in Eqs. (.) (.7). CTECSM ˆ ˆ CDD ˆ CDD ˆ RHD ˆ ( ) DH u... (.) t CTECA ˆ ˆ CDD ˆ CDD ˆ HDD ˆ HDD ˆ ( ) ( ) RHD ˆ 6 DH u t.. (.) CTECW ˆ ˆ HDD ˆ HDD ˆ RHD ˆ ( ) DH u. (.6) t CTECS ˆ ˆ CDD ˆ CDD ˆ HDD ˆ HDD ˆ ( ) ( ) RHD.. (.7) ˆ 6 DH u t where CTECSM, CTECA, CTECW, and CTECS are commercial demand in summer, autumn, winter, and spring, respectively. The ˆ is intercept, meanwhile other ˆ values are regression coefficients. Other variables are the same as in the initial model, Eq. (.).
Temperature ( C) Chapter. Regression-Based Models for Developing Commercial Demand Characteristics Investigation T ma x T mean T min Note: ( ) Mean demand T ref lines - Jun - Aug Sep - Nov Dec - Feb Mar - May (.7) (.88) (.) (.7) SM A W S. Result and Analysis Time period Fig.. The typical of temperature limits for each season: SM = summer, A = autumn, W = winter, S = spring... Demand characteristics with all period Table. presents the best regression results (regression coefficients and statistical tests) among options for initial model. As concerning tested T ref, obtained results are not significantly different. However, from the tested value (T ref = T ref = T ref ), 9 C gives better result for initial model (CTEC) from the assessment by Akaike Information Criterion (AIC) test, Schwarz Criterion (SC) test, and adjusted coefficient of determination R. The AIC and SC values are the lowest among model options, meanwhile the R value is the largest one. In the Table., the value of R and R of model are almost 9%. As R has value between % and %, it indicates that the implemented variables can explain commercial demand well. Application of p-value for % significance level shows that explanation variables have significance as obtained p-values are, less than.. For Prob. (F- Statistics), the value of pointed out that at least one of the used variables influence commercial demand. In addition, from Durbin-Watson (D-W) statistic value, initial model does not contain serial correlation as its value is around. To confirm the nonexistence of heteroskedasticity, corrected standard errors regression is performed in the model [7]. The
related adjusted standard errors are also shown in the Table.. Table. Regression results of all period demand model All Period Demand Model Expl. Variable Coef. CTEC Model (T ref = 9 C) Prob. Adjs. t-statistic (p-value) standard error.76 8.9. CDD..88. CDD(-)..6.9 HDD..8.6 HDD(-)... RHD..96 9.7E- DH -.7-6.8.8 AR().669..6 AR().69 6.99.8 Note: R =.8988; R =.8988; SE Reg. =.8; D-W =.; Prob. (F-Stat.) =.; AIC = -.7; SC = -.79 Concerning coefficient values for meteorological variables, CDD has the highest influence on commercial demand with coefficient value is., and followed by HDD, CDD(-), HDD(-), and RHD. For temperature functions, obtained coefficient ratio for CDD to HDD (α /α ) [8] is about.67. It reflects demand can increase easier under hot than under cold temperature. Likewise the influence of one hour previous temperature, variable of CDD(-) affects demand about. times of HDD(-). For humidity, it has the lowest effect on demand. As regression coefficient for dummy holidays (α 6 ) is negative, volume of demand is lower in holidays than in weekdays... Demand characteristics with half-year models The best results for half-year models which are specified with autoregressive order two for each category are shown in Tables... From Tables. and., adjusted coefficient of determination values R of half-year models are almost same for both categories. However, structure of the best half-year models for Category- started from May to October (CTEChy a ), and from November to April (CTEChy a ) is simpler than another
Relative humidity (%) Chapter. Regression-Based Models for Developing Commercial Demand Characteristics Investigation category. We select Category- as optimum half-year models as simpler models are commonly preferred. In this regards, the half-year models (CTEChy a and CTEChy a ) analyze demand under two different meteorological conditions. Naturally, temperature values in CTEChy a are higher than CTEChy a as CTEChy a period is hot season. Besides, all monthly average humidity values (RHD mean ) in the CTEChy a period tend to higher than in the CTEChy a period as seen in Fig..6. Therefore, CTEChy a refers to the characteristics of demand under period of hot temperature and high humidity, and on the contrary for CTEChy a. 9 8 7 RHD mean (June 8 May 9) RHD min RHD mean RHD max 6 RHD mean (June 7 May 8) Jun Jul Aug Sep Oct Nov 6 Dec 7 Jan 8 Feb 9 Mar Apr May Month Fig..6 Humidity values for each month between June and May 7. In the Table., 9 C and 6 C are optimum T ref for CDD in CTEChy a, and HDD in CTEChy a, respectively. Statistical results in the tables show both models validated well. By separating the period, R value increases slightly in the CTEChy a (9.88%) and decreases in the CTEChy a (8.%) when we compared with CTEC model (89.88%). CTEChy a has higher fitness degree than CTEChy a model. For intercept values ˆ, it is obtained larger in the CTEChy a (.87) than in the CTEChy a period (.66). These values are associated with commercial base demand in the related period. Among meteorological variables applied for CTEChy a and CTEChy a models, CDD (.68) and HDD (.78) variables have largest effect on demand, respectively as in the Table.. However, comparing the coefficient values (CDD in CTEChy a, and HDD in CTEChy a ), the demand has response higher in hot than in cold
temperature. For humidity RHD, it gives the lowest influence on commercial demand, and Table. Regression coefficients of the half-year models (Category-) Expl. Variable ˆ CDD CDD(-) HDD HDD(-) RHD DH AR() AR() CTEChy (T ref = 9 C) Coef. Half-Year Demand Model Prob. (p-value) Table. Regression statistics of the half-year models (Category-) Half-Year Model R R SE Reg. D-W AIC SC CTEChy.977.976.99. -.7 -.6 CTEChy.898.897.7. -.98 -.9 Notes: Prob. (F-Stat.) both CTEChy and CTEChy =. CTEChy (T ref = 6 C) Coef. Prob. (p-value).66.86 (.8).6* (7.).6*.7.6 (.9).* (.9).*...97 (.96).* (.).*..8 (9.9).* (.).8*.8..6 (.).* (.7).7*... (.).* (.).* -.87 -. (-.8).* (-.8).7*.66.67 (9.).* (.89).7*.77.98 (.8).9* (.9).7* Notes: CTEChy = from June to November; CTEChy = from December to May; () t-statistic; *adjs. standard error
Table. Regression coefficients of the half-year models (Category-) Expl. Variable ˆ CDD CDD(-) HDD HDD(-) RHD DH AR() AR() CTEChy a (T ref = 9 C) Half-Year Demand Model Table. Regression statistics of the half-year models (Category-) Half-Year Model R R SE Reg. D-W AIC SC CTEChy a.989.988.978. -. -.98 CTEChy a.86.8..96 -.9 -.978 Notes: Prob. (F-Stat.) both CTEChy a and CTEChy a =.; Without RHD in CTEChy a model, R = 8.% CTEChy a (T ref = 6 C) Coef. Prob. Prob. Coef. (p-value) (p-value).66.87 (8.6).6* (7.).*.68 (.7).*. (.8).9*.78 (.).7*. (.6).6*. 8.E-.8 (6.9).* (.7).* -.87 -.6 (-.6).* (-.9).*.669.698 (8.67).* (.).6*.696.7 (.8).7* (.7).* Notes: CTEChy a = from May to October; CTEChy a = from November to April; () t-statistic; *adjs. standard error; _not significant related to its variable affects demand only in the period of CTEChy a (high humidity). Elimination of the nonsignificance variable (RHD) in CTEChy a model is proper as obtained regression results 6
are almost same. For holidays DH, it causes commercial demand decreases within holidays, but in different quantity for both models... Demand Characteristics with Seasonal Models Tables.6,.7, and.8 present best results for each seasonal model with optimum T ref. The T ref value for summer and autumn models is 9 C, and 6 C for winter and spring models. Optimum T ref values tend to high under hot seasons, and vice versa. From results, the R values are around 8.% to 9.9%. It implies applied variables can explain 8.% to 9.9% seasonal variation of the commercial demand. In this case, the R values for models under hot seasons (CTECSM and CTECA) are higher than the models under cold seasons (CTECW and CTECS). The highest R is obtained in summer, and the lowest one is in winter. However, as R values exceed 8% and three of them are above 86%, the four seasonal models have quite good fitness degree. Next, among applied variables in the models, CDD(-) and HDD(-) in spring model (CTECS) have no significance at % significance level. As temperature condition in spring months is not so hot or so cold (comfortable season), it may relate to the non-significance variables of one hour previous temperature namely CDD(-) and HDD(-) on demand. For simplification, CDD(-) and HDD(-) variables can be eliminated in the CTECS model without influence on regression results. This represents effect of previous temperature values which is commonly in short time period have significance on demands not in all seasons. From demand data, the highest normalized mean demand is in the summer and then followed by winter, autumn, and in spring. Utilization of cooling or heating equipments in business places which is higher in summer and winter than in other two seasons can contribute to the situation. For seasons with severe temperature, the intercept values of ˆ which represent base demand are obtained larger in winter (.9) than in summer (.69). Meanwhile for autumn (.6) and spring (.67), their base demand are between summer and winter values. As utilization of lighting may contribute to base demand, daylight duration is approximately hours in the autumn and spring periods. Regarding ˆ coefficients which quantify effect of applied variables to demands, coefficients for meteorological variables in summer (CDD, CDD(-), RHD) are bigger (give higher influence on demand) than in 7
winter (HDD, HDD(-), RHD). The highest coefficient value for summer is CDD (.9), meanwhile for winter is HDD (.6). Next, for seasons without severe temperature which implement both CDD and HDD, coefficient value for CDD is obtained larger than HDD in autumn (CTECA), and in contrast in spring model (CTECS). It implies dominant temperature in autumn and in spring is CDD and HDD, respectively in terms of as a driver variable. However, compared between dominant temperature variables, CDD (.) in autumn is larger than HDD (.9) in spring. As driver variables, in summer months, not only temperature is high (in terms of hot) but also humidity. On the other hand, in winter months, only temperature variable is high (in terms of cold). Peak periods for summer and winter occur in July or August and January, respectively. Meanwhile, off-peak period for Table.6 Regression coefficients of summer and autumn models with optimum T ref Expl. Variable ˆ CDD CDD(-) HDD HDD(-) RHD DH AR() AR() Seasonal Demand Model CTECSM (T ref = 9 C) CTECA (T ref = 9 C) Coef. Prob. (p-value) Coef. Prob. (p-value).69.6 (7.79).76* (9.8).7*.9. (.9).* (9.69).7*.9.9 (7.7).* (.).7*.8 (.6).*.8 (.9).*..9 (.9).* (.9).* -. -. (-.8).6* (-.8).7*.67.668 (8.).* (.).*.96.9 (8.).* (6.68).* Notes: () t-statistic; *adjs. standard error 8
Table.7 Regression coefficients of winter and spring models with optimum T ref Expl. Variable ˆ CDD CDD(-) HDD HDD(-) RHD DH AR() AR() Seasonal Demand Model CTECW (T ref = 6 C) CTECS (T ref = 6 C) Coef. Prob. (p-value) Coef. Prob. (p-value).9.67 (9.).* (9.9).*.9 (7.).*..6 (.96).*.6.9 (.7).* (9.8).9*..67.8.7 (.9).9* (.8).* -... (-.9).* (9.8).* -.8 -.8 (-9.6).6* (-.).*.699.6998 (.9).* (6.8).6*.7. (8.).* (9.6).9* Notes: () t-statistic; *adjs. standard error; _ not significant related to its variable Table.8 Regression statistics of the seasonal models Reg. Statistics Seasonal Model CTECSM CTECA CTECW CTECS R.9.8986.86.86 R.99.898.8.86 D-W.66.9.87.88 SE Reg...79.78.7 Prob. (F-Stat.).... AIC -.7 -.68 -.676 -.9 SC -. -.679 -.67 -.6 Notes: Without CDD(-) and HDD(-) in CTECS model R = 86.%; R = 86.9% (8); R = 8.86% (9) 9
autumn is in October, and in May for spring. Regarding humidity RHD, it may reduce from the winter model. Based on the information from Japanese calendar for year 8, the number of holidays in all season periods are same namely days excluding in winter ( days). Comparing seasonal models, holidays DH gives highest decreasing effect for summer demand, and on the contrary for spring demand.. Conclusion Regression-based models for developing commercial electricity demand characteristics investigation is presented in this chapter. Two demand models are developed depending on the periods, that is half-year and seasonal models. To carry out the analysis, meteorological variables and existing holidays are considered affect electricity consumption for commercial area (Com. T) in one typical city in Japan. As results, more specific characteristics of the demand can be revealed by proposed models. Though considered variables are the same, structure of the best models (which represents involved key variables) is relatively different in each period. Optimum T ref for CTEChy a, CTECSM, and CTECA models is 9 C, and 6 C for other three models. It indicates optimum T ref related to demand may change by periods. The T ref value tends to high under hot weather period, and vice versa. R values which is around 8.% to 9.88% for half-year models, and around 8.% to 9.9% for seasonal models imply that variables affect commercial demand differently for each period. As R values are relatively high in CTEChy a, CTECSM, and CTECA models, the implemented variables can explain optimally demand in hot rather than in cold weather. For base demand, it is higher in cold than in hot seasons. Next, CDD and HDD are the most significant meteorological variables for commercial demand. Regarding holidays, it will cause demand decreases in each period but in difference amount.
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